To reproduce the problem:
1) set up Zabbix server and database server on different hosts;
2) run the database server and Zabbix server, check that they work;
3) unplug the database server from network;
4) wait for e.g. 30 seconds;
5) plug the database server to the network;
6) see Zabbix server logs - it didn't try to reconnect to the database server.

It seems that when Zabbix server and database server reside on the same host,
the connection is reestablished automatically, but I am not sure.

This issue in particular makes trouble when database server is a high availability cluster.